The clinical symptomology of sickle cell disease is primarily a manifestation of abnormal events in the capillaries. Sickle blood undergoes rheological and shape changes if the oxygen level falls low enough and sufficient time is available for these changes to occur. As oxygen is released in the capillaries by the red blood cells, a "vicious cycle" may ensue, in which the resulting rheological changes decrease the Hb SS cell velocity, leading to a further reduction in oxygen level, greater rheological changes, a further reduction in velocity, and so on. The potential end result is a static mass of sickled cells, blocking circulation. Sickle blood has a number of characteristics that tend to lower oxygen levels in the capillary. On the other hand, aspects of these very same, or other characteristics, tend either or both to maintain high oxygen levels and short residence or transit times, or to mitigate against the consequences of unfavorable changes in either. Consequently, the actual oxygen levels, cell velocities and transit times depend on the interplay or balance between these opposing tendencies. The P.I. has developed a quantitative model of coupled oxygen transport and cell motion in a capillary which incorporates many of the most relevant characteristics of Hb SS blood. A Krogh model is used to model the oxygen transport; the motion of the Hb SS RBC is assumed to be determined by lubrication theory. Although this model already predicts oxygen levels and cell transit times and the circumstances which lead to adverse changes in these, further refinement and extension of the model is necessary before realistic statements about what might happen in vivo can be made. These refinements and extensions are: (1) the incorporation of additional aspects of Hb SS blood, (2) a viscous fluid-filled elastic shell model to replace lubrication theory for the RBC motion, and (3) the use of the single capillary results to develop a network analysis of a capillary bed. The preliminary results suggest that whereas the compensatory mechanisms in sickle cell disease are adequate under normal conditions, they may fail under conditions of reduced pressure gradient across te capillaries; should this result continue to hold for the improved model it would suggest the possible use of arteriolar vasodilators prophylactically, or in the treatment of sickle cell disease.